In this paper, we estimate two small macroeconomic models for the US\ and Germany and we compare the implied optimal monetary policy rules. We consider a model which has been used extensively in the literature (including a Phillips curve, an I-S curve, and a monetary policy rule) and which incorporates some forward-looking features.\ We estimate this model over the period from 1968 to 1998, using the full-information maximum-likelihood procedure, so that forward-looking expectations are fully model-consistent. On the basis of stability tests, the model is shown to have some robustness with respect to the Lucas critique. Then, we compute optimal monetary policy rules in the class of Taylor rules with interest-rate smoothing.\ We find that optimal policies imply a strong degree of interest-rate smoothing. Moreover, German optimal monetary policy is found to require a more persistent and slightly stronger response to inflation and output than the US optimal policy. Last, we provide evidence on the robustness of the German optimal monetary policy to parameter uncertainty.